Novel Nonconforming Finite Element Methods for Maxwell's Equations

麦克斯韦方程组的新颖非协调有限元方法

• 批准号: 0713835
• 负责人: Susanne Brenner
• 金额: $ 26万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-15 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0713835&HistoricalAwards=false
• 关键词: Novel; Nonconforming; Finite; Element; Methods

The research in this project is based on the recent discovery of the PIs that numerical solutions of Maxwell's equations can be based on variational formulations that use function spaces where the divergence free condition is enforced. This is made possible by combining classical nonconforming finite elements for incompressible fluid flows and techniques from discontinuous Galerkin methods. In this new approach the boundary value problems of the time-harmonic (frequency-domain) Maxwell's equations are solved as elliptic problems, and the performance of the new nonconforming finite element methods for both the source (deterministic) problem and the eigenproblem (cavity resonance problem) is comparable to the performance of classical finite element methods for computational mechanics. In particular the discrete eigenvalues have neither spurious modes nor nonphysical zero eigenvalues. The proposed research will design and analyze many novel schemes for the Maxwell equations and the Maxwell eigenproblem using this new approach. Fast solvers (multigrid and domain decomposition methods) and adaptive algorithms will also be developed, with applications to related electromagnetic problems.The results of the proposed research will provide powerful computational tools for the design and analysis of electromagnetic devices such as antennas, radar sensors, waveguides, photonic crystals, magnetoresistive sensors and particle accelerators, with applications to diverse areas such as telecommunications, integrated optics, lasers, high energy physics, plasma physics, and nondestructive damage detection.

在这个项目中的研究是基于最近发现的PI的数值解的麦克斯韦方程可以基于变分公式，使用的功能空间的发散自由的条件是强制执行。 这是可能的，结合经典的不可压缩流体流动和间断伽辽金方法的技术的有限元。在这种新的方法中，时间谐波（频域）麦克斯韦方程的边值问题被解决为椭圆问题，和新的有限元方法的性能的源（确定性）问题和本征值问题（空腔共振问题）的计算力学的经典有限元方法的性能相媲美。特别是离散本征值既没有寄生模式，也没有非物理零本征值。拟议的研究将设计和分析许多新的计划，麦克斯韦方程组和麦克斯韦特征值问题，使用这种新的方法。快速求解器研究结果将为天线、雷达传感器、波导、光子晶体、磁阻传感器和粒子加速器等电磁器件的设计和分析提供强有力的计算工具，并可应用于电信、计算机科学等多个领域。集成光学、激光、高能物理、等离子体物理和无损检测。